Theory of quadratic optical frequency combs

Abstract

We present theoretical studies of optical frequency comb generation in dispersive quadratically nonlinear resonators. We introduce a mean field equation approach to model cavity enhanced second harmonic generation and find excellent agreement with recent experimental frequency comb observations. We also develop a more general approach based on a single envelope equation for both quadratic and Kerr nonlinear cavities. Keywords: nonlinear optics, parametric processes, parametric oscillators, optical resonators. INTRODUCTIONThe generation of an optical frequency comb (OFC) by means of a nonlinear microresonator shows promise for enabling chip scale devices that can complement current comb sources based on bulk mode-locked lasers [1]. Microresonator-based OFC sources can provide a direct link between optical and microwave frequencies and have a host of potential applications to metrology, including ultra-precise optical clocks, biomedical and environmental spectroscopy, microwave photonics and multi-user coherent optical communications.A substantial boost to the advancement of the theory and numerical modelling of Kerr microresonator OFCs has been provided by the realization that one can model the dynamics of the system using a time-domain description. This approach is based on the mean-field driven and damped nonlinear Schrödinger equation [2], which was earlier derived for coherently pumped passive fiber cavities [3].Most research to date has focused on coherently pumped cubic Kerr nonlinear microresonators, where the physical principle of OFC generation is cascade four-wave mixing activated by modulation instability. However, modulation instabilities and pulse trains can also be obtained from quadratic nonlinear cavities [4], that could allow frequency comb generation in wavelength ranges where pump sources are unavailable, in particular in the mid-infrared. At the same time, quadratic comb sources can also lead to a substantial decrease in the required pump power level and allow for chip scale integration.In fact, recent experiments have demonstrated the possibility of achieving OFC generation through the singly resonant cavity second harmonic process [5,6]. In this work, we review our development of the theory of OFC generation in quadratic cavities and microresonators, based on time-domain nonlinear evolution equations with different levels of complexity [7][8][9][10]. To validate our theory, we show that an excellent agreement between the theory and the experimental results is achieved.